On September 8th 1974 Robert Craig "Evel" Knievel attemted to fly across
Idaho's 1600 ft wide Snake River Canyon in a steam powered rocket called
the X2 Skycycle.The attempt failed due to pre mature parachute deployment.
The X2 landed inside the canyon with a battered Evel Knievel inside.

Lagari Hasan had the Evil one beat by almost 300 years (1633). Hasan's top altitude (non verifiable obviously) was about 300 meters, so Knievel may have taken the altitude record from him, but then again who was counting.

If Hasan has managed to make it all the way across the Bosporus, he probably would have died, but if on some small chance he'd lived, he would have made the first intercontinental flight.

Since the flight was technically made for royalty, and since there was no such thing, strictly speaking, as capitolism in the early 17th century Ottoman empire, I don't know if his flight can be technically considered "Private" but it comes close enough to give the guy some slack.